What does the suffix -stan mean in words like "Afghanistan" and "Pakistan?"

-Stan is formed from the old Iranian root *sta- "to stand, stay," and means "place where one stays," i.e. homeland or country. Names such as Afghani-stan, Tajiki-stan, Hindu-stan are formed by adding this suffix to the usually pluralized names of the people living in that country, as the Afghani (one Afghan) live in Afghanistan. However, Pakistan was formed from the initial letters of "Punjab," "Afghanistan," and "Kashmir" and the questionably extended suffix -istan. So, now there is an extended suffix floating around that may be added to new countries, the name of whose people is not pluralized by the suffix -i.

By the way, Iranian is the mother language from which the modern Persian or Farsi, Pashto, Baluchi, etc. languages developed. The Germanic language family, of which English (German, Swedish, Dutch, etc.) is a member, developed from the same great-great-grandmother, Proto-Indo-European(PIE) some 7,000 years ago, so the same root also turns up in English "stand," "stay," "steady," and others.